This invention is in the field of oil and gas production. Embodiments of this invention are more specifically directed to the analysis of production field measurements for purposes of well and reservoir management.
The current economic climate emphasizes the need for optimizing hydrocarbon production. Such optimization is especially important considering that the costs of drilling of new wells and operating existing wells are high by historical standards, largely because of the extreme depths to which new producing wells must be drilled and because of other physical barriers to discovering and exploiting reservoirs. These high economic stakes require operators to devote substantial resources toward effective management of oil and gas reservoirs, and effective management of individual wells within production fields.
For example, the optimization of production from a given field or reservoir involves decisions regarding the number and placement of wells, including whether to add or shut-in wells. Secondary and tertiary recovery operations, for example involving the injection of water or gas into the reservoir, require decisions regarding whether to initiate or cease such operations, and also how many wells are to serve as injection wells and their locations in the field. Some wells may require well treatment, such as fracturing of the wellbore if drilling and production activity have packed the wellbore surface to the extent that production has slowed. In some cases, production may be improved by shutting-in one or more wells for an extended period of time, in which case the optimization of production may require reconfiguring the entire production field. All of these actions are performed with an eye toward maximizing production at minimum cost. As evident from these examples and as known in the art, the optimization of a production field is a complex problem, involving many variables and presenting many choices.
This problem is exacerbated by the complexity and inscrutability of the sub-surface “architecture” of today's producing reservoirs. As mentioned above, current-day oil and gas reservoirs are often at extreme depths or in otherwise difficult geographical locations, both on land or offshore, because those reservoirs that are easy to reach have already been developed and produced. These extreme depths and relative inaccessibility limit the precision and accuracy of the necessarily indirect methods used to characterize the structure and location of the hydrocarbon-bearing reservoirs. In addition, the sub-surface structure of many reservoirs presents complexities such as variable porosity and permeability of the rock, and such as fractures and faults that compartmentalize formations in the reservoir and complicate sub-surface fluid flow. As known in the art, the ability of conventional exploration technologies of seismic prospecting, magnet surveying, and gravitational surveying to accurately portray the structure and contents of sub-surface strata becomes poorer as the depth of interest increases.
Accordingly, while seismic exploration and similar techniques provide important information from which the structure and properties of the sub-surface can be inferred, that information has, at best, a relatively coarse spatial resolution. The resolution of these surveys is even coarser for those regions in which salts and similar features or strata attenuate or distort seismic energy. As a result, the understanding of the structure and connectivity of sub-surface features provided by seismic and similar surveys is necessarily imprecise.
Conventional well logs provide important information regarding the location and properties of sub-surface strata during and after the drilling of exploratory, development, and production wells. These well logs yield direct information regarding depths, thicknesses, and material properties of sub-surface formations and strata. However, the information gained from well logs is valid only at the specific location of the well, and provides little visibility into the reservoir at any significant distance away from the well. Furthermore, as the depths of interest for newly developed formations increase, so does the cost of drilling and logging exploratory wells. For these reasons, well logs provide only limited insight into the sub-surface structure, architecture, and connectivity of many newly-developed and producing reservoirs.
In recent years, advances have been made in improving the measurement and analysis of parameters involved in oil and gas production, with the goal of improving production decisions. For example, surface pressure gauges and flow meters deployed at the wellhead, and also in surface lines interconnecting wellheads with centralized processing facilities, are now commonly monitored on virtually a continuous basis. Furthermore, reliable downhole pressure sensors are now often plumbed into the production string and left in the wellbore during production. The improved reliability of these sensors, even at elevated downhole temperatures and pressures, has enabled widespread deployment of real-time downhole pressure sensors that continuously monitor downhole pressure during production.
As known in the art, the manner in which downhole pressure and flow rate evolve over time provides insight into the reservoir pressure in the region around the well. Reservoir pressure is an important parameter in understanding the reservoir and how to optimize production, because the rate at which oil or gas will flow into the wellbore downhole (and thus out of the well at the surface) strongly depends on the difference between the reservoir pressure and the back pressure exerted by the fluid in the wellbore. Over time, the volume of oil or gas drawn out of the well will generally reduce the reservoir pressure and the rate of production will fall.
The evolution of well downhole pressure and flow rate over time depends on the rock properties (e.g., permeability, porosity, etc.) throughout the reservoir, on barriers to flow within the reservoir, and on the reservoir boundaries. As such, it is possible to obtain information about these properties by analyzing the transient behavior of downhole pressure and the rates of producing wells.
While these downhole pressure measurement data are theoretically valuable in understanding reservoir behavior, the ability of conventional techniques to characterize and evaluate reservoir architecture and connectivity remains somewhat limited. As known in the art and as mentioned above, the evolution of downhole measured pressure with time is closely related to the flow rate from the well, as well as dependent on the reservoir properties of permeability, reservoir heterogeneities, faults, boundaries, and dependent on the overall shape and volume of the reservoir compartment being drained by the well, as mentioned above. Because the goal of pressure analysis is to understand the reservoir properties, it is desirable to minimize the effects of flow rate variation on the well pressure behavior, which can be done by flowing the well at a constant well rate. In this case, the response of downhole pressure to a constant flow rate is a useful characteristic because it reflects the reservoir properties and is not affected by rate changes. Unfortunately, it is difficult to maintain the flow rate of a well precisely constant for an extended period of time. Rather, well flow rates typically change over time. Furthermore, the pressure response to changes in flow rate has a very long time constant, and as such long-ago periods in the flow rate history of a well affect its current downhole pressure.
One approach to obtaining constant-rate pressure response from a well, for the purpose of characterizing the reservoir, is to carry out a “shut-in” or “pressure build-up” test, after the well has produced for some significant time. This approach of recovering reservoir properties from bottomhole measured pressure data is more generally referred to as pressure transient analysis (“PTA”). According to this approach, the well under analysis is flowed at a reasonable constant non-zero flow rate for some time, and is then shut-in for a period of time while the downhole pressure is measured. Because the well flow rate is essentially constant, at zero, during the “shut-in” period, the transient behavior of bottomhole pressure during the shut-in period primarily reflects the reservoir properties. Several shut-in and draw-down intervals are typically included within a single well test. Techniques are known in the art for recovering the pressure response from these variable-rate data. One conventional approach considers the pressure response to a sequence of flow rates as the superposition of several constant-flow conditions; the resulting pressure response is then plotted over “superposition time”, and can be readily analyzed. However, PTA well tests are costly from the standpoint of lost production, and also require significant operator involvement to carry out the shut-in and operation at a constant flow rate, especially given the time period required for such a test (which can extend over several days or weeks).
During an early period of time after flow starts, reservoir boundaries have no effect on dynamic pressure behavior, because the effects of the well production have not yet reached the reservoir boundaries. Analysis of the pressure response under this “infinite-acting” assumption is useful in characterizing properties of the formation near the well, and is valid for a radius of interest until the effects of the reservoir boundary appear. After such time as the effects of reservoir boundaries on the pressure response are observed, conventional pressure-transient analysis of the “boundary-dominated” response can provide some insight into those boundaries. For example, the time at which the pressure response deviates from that expected under the infinite-acting assumption can indicate the distance of a reservoir boundary from the wellbore. In addition, attributes of the pressure response under boundary-dominated conditions can indicate whether the boundary is of a “no-flow” type, or if instead the boundary is abutted by some other source of pressure, such as an aquifer. However, the ability of conventional pressure transient analysis to provide significant information regarding the detailed structure of the reservoir is limited by the absence of directionality in the pressure measurements. The extremely long well test time required to detect and analyze these boundary effects also limits the quantity of valid analyzable boundary-dominated pressure response data.
Pressure-rate deconvolution is another known approach to identifying the constant-rate pressure response of a given well, from downhole pressure measurements gathered during production or other time periods in which the flow rate is in fact not constant. A detailed discussion of pressure-rate deconvolution is presented in Levitan et al., “Practical Considerations for Pressure-Rate Deconvolution of Well-Test Data”, SPE Journal (March 2006), pp. 35-47, incorporated herein by reference. Pressure-rate deconvolution is based on the relationship of time-varying pressure pi(t) at well i to the time-varying well flow rate qi(t), expressed in the form of a convolution integral:
                                          p            i                    ⁡                      (            t            )                          =                              p            i            0                    -                                    ∫              0              t                        ⁢                                                            q                  i                                ⁡                                  (                  τ                  )                                            ⁢                                                                    ⅆ                                          P                      ⁡                                              (                                                  t                          -                          τ                                                )                                                                              ⁢                                                                                                          ⅆ                  τ                                            ⁢                                                          ⁢                              ⅆ                τ                                                                        (        1        )            In this convolution integral, dP(t)/dt is the time-dependent behavior of downhole pressure in response to production at a unit flow rate, beginning from an initial pressure pi0 at time-zero. It is this downhole pressure response dP(t)/dt to an arbitrary unit of flow rate that is useful in characterizing the properties of the formation, as known in the art. The above-referenced Levitan et al. article describes a method for deconvolving the time-varying flow rate from the time-varying pressure behavior from the convolution integral, to yield this downhole pressure response. While pressure-rate deconvolution extends the time of analysis, and thus extends the radius of investigation, from that provided by superposition and other PTA approaches, the flow rate and pressure data are still subject to certain constraints on data quality and consistency in order to satisfy the assumptions underlying the convolution integral. The time over which data suitable for pressure-rate deconvolution can be gathered and reasonably deconvolved remains limited to that provided by a conventional well test, which typically does not run beyond two weeks or so. In typical production fields, this limited test duration limits the radius of investigation to about several thousand feet from the well.
As mentioned above, conventional well tests are performed on individual wells, one at a time. However, in typical production fields, multiple wells are producing from the same formation at the same time, and the flow from each well producing from a given formation not only affects the wellbore pressure for that well, but also affects the wellbore pressure in other wells producing from that same formation and from other formations connected to that well. Accordingly, for pressure-transient analysis or single-well pressure-rate deconvolution to be valid for a particular well, the well test must either be performed with all other nearby wells shut-in, or the radius of investigation must be sufficiently limited so that the effects of neighboring wells are not a factor. These constraints thus dramatically increase the cost of a well test (and thus reduce the frequency of such testing), and decrease the usefulness of the well test in exploring formation structure and connectivity.
As mentioned above, real-time downhole pressure measurements are now commonly acquired during production. To avoid the cost of well tests, it is desirable to use the large volume of pressure and rate data acquired during production from the field. However, conventional pressure transient analysis is limited in its ability to analyze these not-so-well-behaved pressure and rate data acquired during production. In addition, the complexity presented by the inter-well effects mentioned above also overwhelms these conventional approaches.
By way of further background, a more general expression of the pressure-rate convolution integral in the case of multiple wells drawing from the same formation or reservoir is provided in Levitan, “Deconvolution of Multiwell Test Data”, 2006 Annual Technical Conference and Exhibition, Paper No. SPE 102484 (2006), incorporated herein by reference. That expression is:
                                          p            i                    ⁡                      (            t            )                          =                              p            i            0                    -                                    ∑              j                        ⁢                                                  ⁢                                          ∫                0                t                            ⁢                                                                                          ⅆ                                                                        P                          ij                                                ⁡                                                  (                          τ                          )                                                                                      ⁢                                                                                                                      ⅆ                    τ                                                  ⁢                                                      q                    j                                    ⁡                                      (                                          t                      -                      τ                                        )                                                  ⁢                                                                  ⁢                                  ⅆ                  τ                                                                                        (        2        )            where well i represents the well of interest, and where index j refers to each well in the production field (the set of j wells including well i itself). According to this convolution interval, a pressure response term
      ⅆ                  P        ij            ⁡              (        τ        )                  ⅆ    τ  refers to the pressure response at well i to a unit flow rate produced from well j, where well i is included in the set of wells j (i.e.,
      ⅆ                  P        ii            ⁡              (        τ        )                  ⅆ    τ  corresponds to the single well pressure response used in conventional pressure-rate deconvolution for single well analysis). According to this approach, the generalization of pressure-rate deconvolution to the multi-well case allows reconstruction of the matrix Pij of constant-rate pressure interference responses from the pressure and rate data acquired from several producing wells in the field. Analysis of these responses enables one to draw conclusions about the reservoir properties in relation to each of the wells involved. This brings directionality into consideration, and thus enables the recovery of more detailed information about reservoir properties, including information regarding its connectivity, shape, architecture, and volume.
Despite all of the limitations to measurement of reservoirs and sub-surface properties, reservoir management decisions must still be made, and therefore will be made using the best available yet incomplete understanding of the structure of the reservoir. As mentioned above, these reservoir management decisions include whether and where to place additional production wells, whether and where to inject gas or other substances for secondary recovery operations, and the like. Well management decisions, such as whether, when, and how to workover an existing production well to improve its production output, must also be made, even if based on a limited understanding of the reservoir. And, of course, short-term and long-term economic analysis of the reservoir is also important to the operator and the financial backers of the project.
In order to make these decisions, reservoir engineers commonly develop models of reservoir behavior. Conventional reservoir models are based on seismic and other geological surveys of the production field, along with conclusions that can be drawn from well logs, pressure transient analysis, and the like. These models are applied to conventional reservoir “simulator” computer programs, by way of which the reservoir engineer can analyze the behavior of the reservoir under production conditions, and by way of which the engineer can simulate the behavior of the reservoir in response to potential reservoir management actions (i.e., “what-if” analysis). Some reservoir simulators approximate fluid flow in the reservoir on a grid of geometric elements, and numerically simulate fluid flow behavior using finite-difference or finite-element techniques to solve for pressure and flow conditions within and between elements in the grid. Simulation of the reservoir behavior is then attained by stepping in time and evolving the inter-element flows and the pressures at each grid element over a sequence of the time steps. However, serious limitations in these conventional finite-element and finite-difference models and simulator techniques preclude their ability to simulate the pressure transient behavior in the wellbore to an extent that could be directly compared with the actual pressure measurements obtained by downhole gates in the wells.
In order to optimize the management of a reservoir, it is desirable for reservoir engineers to validate the reservoir models and simulators based on measurements of the actual performance at the wells. Such validation of the reservoir models allows the reservoir engineer to modify and thus improve the model in response to discrepancies between expected and observed behavior, with the goal of improving the fidelity of the model to the reservoir as observed. However, given the limitations described above, it is difficult to correlate reservoir simulations with measurements of flow rate, temperatures, downhole pressure, and the like obtained during production and during shut-in and draw-down events. On one hand, as described above, the resolution of seismic and other conventional geological surveys is relatively coarse. Conventional finite-element and finite-difference simulators also have relatively coarse resolution, in that the pressure and flow estimates generated by the simulators are averages over each grid element. To maintain reasonable computing times for the simulators, even with today's high-speed computers, the resolution of the grid elements cannot be much smaller than 100 feet, considering that the number of computations required for such simulators typically scale with the cube of the number of grid elements. On the other hand, downhole pressure measurements obtained from the wellbore are spatially precise, in that the sensed pressure is the pressure only at the wellbore location (i.e., corresponding to the pressure within only a small radius of the wellbore, such as one foot), and are not necessarily representative of the average pressure of the surrounding volume at a radius of 100 feet. Therefore, even if the model were accurate, the simulated reservoir pressure for a grid element may not match the measured reservoir pressure at the precise location of the well within the grid volume.
To summarize, conventional reservoir modeling and data gathering and analysis techniques are limited in several ways. These conventional approaches are generally limited to the single-well situation, and thus cannot comprehend the real-world situation of multiple wells producing from the same formation. In addition, the time duration that can be analyzed using these conventional approaches is necessarily limited, especially considering that inter-well effects on pressure measurements must be avoided. Accordingly, the visibility of this analysis at significant distances from the wellbore into the formation is limited. In addition, only simple reservoir geometries are suitable for analysis by these conventional techniques.
Unfortunately, these complexities are in fact present in many reservoirs, especially in those oil and gas reserves that are currently being developed at extreme depths and at remote locations. As such, substantial differences between reservoir behavior as predicted by the model and reservoir behavior as observed via downhole pressure measurements and other measurements often result. Therefore, despite the availability of a large amount of real-time downhole pressure data from modern-day production fields, good correlation of that data with conventional reservoir models is seldom attained.
Conventional reservoir models and simulators are also not conducive to efficient reconfiguration and modification. Ideally, reservoir engineers would carry out multiple iterations of adjusting the reservoir model in response to discrepancies between observed performance and that predicted by the model, followed by verification of the modified model with the actual reservoir behavior as measured, to ultimately converging to an accurate reservoir model. But known numerical reservoir modeling and simulation techniques are not well-suited for iterative modification in this manner. For example, the numerical approaches of finite-element and finite-difference analysis require re-gridding of the entire reservoir in response to any change in reservoir shape or boundary geometry, no matter how small the change. In addition, long computing times are required to execute these conventional numerical simulators, reducing the ability to interactively modify the model to correspond to observed data, even if good correlation between model and measurements were achievable in the first place.
By way of further background, boundary-element formulations of the pressure-transient analysis problem are described in Kikani et al., “Pressure-Transient Analysis of Arbitrarily Shaped Reservoirs With the Boundary-Element Method”, SPE Formation Evaluation (March 1992), pp. 53-60; and in Kikani et al., “Modeling Pressure-Transient Behavior of Sectionally Homogeneous Reservoirs by the Boundary-Element Method”, SPE Formation Evaluation (June 1993), pp. 145-52, both incorporated herein by this reference.
By way of further background, an approach to pressure transient analysis that is useful in generalized radial and linear models with heterogeneities is described in Levitan et al., “General Heterogeneous Radial and Linear Models for Well Test Analysis”, 70th Annual Technical Conference and Exhibition, Paper No. SPE 30554 (1995), pp. 225-38, incorporated herein by this reference.